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  • The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2. The length of the longest edge is A. 12 cm B. 6 cm C. 18 cm D. 3 cm

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm^3 and the total surface area is 252 cm^2. The length of the longest edge is
A. 12 cm
B. 6 cm
C. 18 cm
D. 3 cm

Answers (1)

The volume and total S.A of a block are given

Let the length, breadth and height of a rectangular block be given by  \frac{a}{r},a,ar  respectively.   

 

 V=L*B *H=\frac{a}{r} \times a \times ar=a^{3} \\\\


\\216=a^{3} \\\\ a=6cm \\\\
   S=2 \left[ L*B+B*H+H*L \right] =2 \left[ \frac{a}{r} \times a+\frac{a}{r} \times ar+a \times ar \right] =2 \left( \frac{a^{2}}{r}+a^{2}+a^{2}r \right) \\\\
   \\ 252=2a^{2} \left( \frac{1}{r}+1+r \right) \\\\\frac{252}{72}=\frac{r^{2}+r+1}{r} \\\\ 2r^{2}-5r+2=0 \\\\ \left( 2r-1 \right) \left( r-2 \right) =0 \\\\ r=\frac{1}{2} \ or \ r=2 \\\\

If a = 6 and r=2 then l,b and h are    \text{3 cm, 6 cm,12 cm}  respectively.   

If a=6 and r=1/2 then l,b and h are 12, 6 and 3 respectively.   

In both the cases, the longest side is 12 units.   

Hence, correct option is a.   

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infoexpert21

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